We report on a study in which plasmid DNA in water was irradiated with 30 keV electrons generated by a scanning electron microscope and passed through a 100 nm thick Si3N4 membrane. The corresponding Monte Carlo simulations suggest that the kinetic energy spectrum of the electrons throughout the water is dominated by low energy electrons (<100 eV). The DNA radiation damage, single-strand breaks (SSB) and double-strand breaks (DSB), was determined by electrophoresis. The median lethal dose of D1/2 = 1.7 ± 0.3 Gy was found to be much smaller compared to partially or fully hydrated DNA irradiated under vacuum conditions. The ratio of DSB to SSB was found to be (1:12) as compared to 1:88) found for hydrated DNA. Our method enables quantitative measurements of radiation damage to biomolecules (DNA, proteins) in solutions under varying conditions (pH, salinity, cosolutes) for an electron energy range which is difficult to probe by standard methods.